In particular this implies that equation (REF ) can arise also as bottom equation of a triplet possessing tetrahedron property.
The relevant triplet is that coming from Case D in Theorem 3.12 in [1]} that in our notation reads as
\(A = v_{n,m,p}v_{n+1,m+1,p}+v_{n+1,m,p}v_{n,m+1,p},  \\B =\lambda (v_{n,m,p} v_{n,m+1,p}+v_{n,m,p+1} v_{n,m+1,p+1})-v_{n,m,p} v_{n,m+1,p+1}-v_{n,m+1,p} v_{n,m,p+1},  \\C=\frac{1}{\lambda } ( v_{n,m,p} v_{n+1,m,p}+v_{n,m,p+1} v_{n+1,m,p+1} )-v_{n,m,p} v_{n+1,m,p+1}-v_{n+1,m,p} v_{n,m,p+1}, \!\!\!\!\) 
